Spectral analysis using the Karhunen-Loeve transform

Decomposing a vector time series into orthogonal components is a well known technique for analysing space or time signals that have a spectral line structure. This paper deals with the resolution capability of the algorithm. The space spanned by the eigenvectors of the data correlation matrix can be decomposed into two subspaces, the first of which contains the periodic signal components. The remaining components in the second subspace have a power spectrum with well pronounced minima at the frequencies of the periodic components. Computer simulations provide insight into the resolution capabilities of this partioning procedure. Higher resolution than the conventional one can be achieved if the correlation matrix can be estimated sufficiently exact.